Question

Find the magnitude and direction angle θ of the following vectors. Round the magnitude to the nearest tenth, and round the direction angle to the nearest degree, if rounding is necessary.
u = (-12, 2)

Answer 1

To find the magnitude of the vector u = (-12, 2), we use the formula for magnitude:

|u| = √(x^2 + y^2)

where x and y are the components of the vector.

|u| = √((-12)^2 + 2^2)
|u| = √(144 + 4)
|u| = √148
|u| ≈ 12.1

Rounding to the nearest tenth, the magnitude of u is approximately 12.1.

To find the direction angle θ, we use the formula:

θ = arctan(y / x)

where x and y are the components of the vector.

θ = arctan(2 / -12)
θ ≈ -9.5°

Rounding to the nearest degree, the direction angle θ of vector u is approximately -9°.